Need help calculating a Residue

I am trying to integrate log(x)/( (1+x^2)^2) and I'm stuck at trying to find the residue of that function at i. I've tried expanding it to find the coefficient of (x-i) but I just get into a mess and as the pole is a double covert pole I don't think there is any nice formula that would lead me to the answer. Can anyone help please?

I am trying to integrate log(x)/( (1+x^2)^2) and I'm stuck at trying to find the residue of that function at i. I've tried expanding it to find the coefficient of (x-i) but I just get into a mess and as the pole is a double covert pole I don't think there is any nice formula that would lead me to the answer. Can anyone help please?